This invention relates to audio apparatus, and in particular audio apparatus for radiating an ultrasonic pressure wave with a modulated audio signal.
Audio spotlighting, using a parametric audio system, provides a means for projecting highly directional beams of audible sound. This technology employs the non-linearity of a compressible material (such as air) to create audible by-products from inaudible ultrasound. This technique exploits an acoustic phenomenon called self-demodulation where low frequency audio beams of high directivity are generated from a high amplitude ultrasonic beam that has been modulated with an audio signal. Self-demodulation generates new frequencies in the received sound spectra based on the envelope frequency (i.e. the required audio signal) in a process akin to AM demodulation. Thus this technique provides a beam of audio sound with the focused directional properties of the original ultrasonic carrier beam, allowing distant targeting of specific listeners. This technique can produce predictable and controllable levels of audio sound and, despite the relatively weak effect of self-demodulation, is capable of generating substantial sound amplitudes due to the narrow spatial distribution of the acoustic energy.
The transmitted modulated ultrasonic wave can be considered as a collimated primary wave consisting of an amplitude modulated wave of pressure where the primary pressure wave is defined by
1) p1=P1E(t)sin(ωct)
where P1 is the amplitude of the primary beam pressure, ωc is the carrier frequency and E(t) is the modulation envelope. For an amplitude modulated signal E(t) is equal to (1+mg(t)) where m is the modulation depth and g(t) is the audio signal.
As a result of p1 interacting with the air the modulated audio signal demodulates creating an audible secondary pressure wave p2 given by                                          p            2                    ⁡                      (            t            )                          =                                            β              ⁢                                                          ⁢                              P                1                2                            ⁢              A                                      16              ⁢              π              ⁢                                                          ⁢                              ρ                0                            ⁢                              c                0                4                            ⁢              z              ⁢                                                          ⁢              α                                ⁢                                    ∂              2                                      ∂                              t                2                                              ⁢                                    E              2                        ⁡                          (              τ              )                                                          2        )            where β is the coefficient of nonlinearity (βair=1.2), ρ0 is the ambient density of the medium, c0 is the small signal wave propagation speed, A is the beam's cross-sectional area, z is the axial distance, α is the absorption coefficient of the medium. So, for example, where c=343 m/s, ρ0=1.2 kg/m3, α=0.6, and A=5×10 m−3, a 140 dB ultrasound wave modulated with a 1 kHz signal would produce about 71 dB of audible sound at 1 m.
The power of the resultant audio signal is proportional to the second derivative of the square of the modulation envelope. As a result significant coloration (i.e. a shift of signal power with respect to frequency) and distortion are introduced onto the demodulated audio signal as a result of the interaction of the ultrasonic wave with the non-linear medium. The coloration of the signal results in the low frequency audio components being suppressed by approximately 12 dB/octave; this is represented by the second derivative term of the modulation envelope. The distortion of the signal is represented by the square of the modulation envelope.
Processing the audio signal prior to modulation can minimize the effects of coloration and distortion that result from the interaction of the ultrasonic wave with the non-linear medium. The processing typically comprises a double integration filter to compensate for coloration of the audio signal and a square root operation to compensate for the distortion of the audio signal.
However, for the self-demodulation to occur high ultrasonic sound pressure levels are required. To generate these high pressure levels it is necessary to generate the ultrasonic pressure levels at or close to the resonant frequency of the transmitting transducer. Correspondingly the frequency response of the transducer can vary dramatically at this frequency. The variable transducer frequency response can significantly affect the quality of the demodulated audio pressure wave.
FIG. 1, plot A shows the frequency spectrum of a white noise input signal constrained between 300 and 4000 Hz prior to modulation with an ultrasonic carrier signal. An example of the effects of self-demodulation and transducer conversion upon the input signal, using a typical transducer having a measured frequency response shown in FIG. 2, is shown in FIG. 1, plot B.
The frequency response of a transducer can be flattened at the resonant frequency. However this requires considerable damping to be added to the transducer, and a corresponding drop in ultrasonic pressure level. This in turn would require a transducer with a large radiating surface area, which is not suitable for small devices, for example a mobile communication device and in particular a radiotelephone.